相关论文: Theory of periodic convolutional neural network

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…

The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…

Convolutional neural networks (CNNs) have been used in many machine learning fields. In practical applications, the computational cost of convolutional neural networks is often high with the deepening of the network and the growth of data…

While the depth of modern Convolutional Neural Networks (CNNs) surpasses that of the pioneering networks with a significant margin, the traditional way of appending supervision only over the final classifier and progressively propagating…

We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specifically, we first introduce a mathematically equivalent form…

The state of the art in many computer vision tasks is represented by Convolutional Neural Networks (CNNs). Although their hierarchical organization and local feature extraction are inspired by the structure of primate visual systems, the…

It is widely acknowledged that trained convolutional neural networks (CNNs) have different levels of sensitivity to signals of different frequency. In particular, a number of empirical studies have documented CNNs sensitivity to…

The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data. We explore artificially constraining the frequency spectra of…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

Deep learning has established many new state of the art solutions in the last decade in areas such as object, scene and speech recognition. In particular Convolutional Neural Network (CNN) is a category of deep learning which obtains…

Convolutional neural networks (CNNs) for image processing tend to focus on localized texture patterns, commonly referred to as texture bias. While most of the previous works in the literature focus on the task of image classification, we go…

We describe the emergence of a Convolution Bottleneck (CBN) structure in CNNs, where the network uses its first few layers to transform the input representation into a representation that is supported only along a few frequencies and…

We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained with $L^2$ weight decay regularization. Our main contributions…

Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t). The approximation can…

Convolutional neural networks (CNNs) are usually built by stacking convolutional operations layer-by-layer. Although CNN has shown strong capability to extract semantics from raw pixels, its capacity to capture spatial relationships of…

These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential…

The latest generation of Convolutional Neural Networks (CNN) have achieved impressive results in challenging benchmarks on image recognition and object detection, significantly raising the interest of the community in these methods.…

Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…

Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…